How common was it for battles/sieges to be determined by single combat between two opposing champions?

by fookin_Pikeys
blolfighter

Reverse question: How common was it for battles/sieges to not be determined in this fashion? By which I mean how often was single combat fought in this fashion, only for the losing side to decide "nah, that didn't count, we're just going to continue what we were doing?" And how often did the winner have to run for his life?

ScipioAfricanvs
realhermit

Going to add to this question, how historically accurate is David vs Goliath?